Such a medical fluid control device is known from U.S. Pat. No. 7,984,730 B2. The known medical fluid control device is designed as a three-way stopcock for a medical infusion system. The three-way stopcock has two connection ports and one injection port which are all formed integrally on a fluid flow housing. The injection port is provided with an openable closure element in the form of a closure cap, which can be fitted by way of a Luer lock connection, or in the form of an elastically flexible closure diaphragm. The closure cap can be twisted off and removed from the injection port. The closure diaphragm is openable in that it can be opened in an elastic manner in the region of an end-side throughflow slot. The closure diaphragm is opened in particular by the attachment of an injector. The fluid flow housing has an adjustment member which is mounted rotationally movably in the fluid flow housing and which is provided with flow channel sections which, depending on the position of the adjustment member, are in fluidic connection, that is to say in throughflow connection, with the two connection ports or with at least one connection port and the injection port. When the closure element is closed, that is to say when the injection port is closed, it is thus possible to divert via the injection port a fluid throughflow in the region of the connection ports and thus bring about flushing of an inner side of the injection port. Consequently, the unwanted deposition of medicament residues in the injection port can be avoided.